James Hong sat in a Silicon Valley bar back in 2000, downing a few drinks with a friend. Talk turned to the physical attributes of a woman they knew, and after some heated—and well-lubricated—debate, they came up with Hotornot.com, a dating website on which users rate one another’s looks with all the sensitivity of frat boys at a kegger.

Hong has since worked almost solely on creating businesses he finds amusing—like Savemyass.com, which sends flowers to a wife or girlfriend on predetermined dates. Early this year, Hong and his partner sold Hotornot for $20 million in cash.

This kind of success makes him seem pretty darn brilliant.

And it sets up a question: What is brilliance, anyway? It is not just about intelligence, success, or fame. Brilliance is a slippery quality; it can be relative, temporary, or a matter of taste. Consider Stephen Schwarzman, who built his investment firm, the Blackstone Group, into a goliath. He took the company public in mid-2007, and when his net worth rocketed to $8 billion on the first day of trading, he was universally hailed as brilliant. Within months, though, the whole thing went south, and Schwarzman's $8 billion dropped to $4 billion. Suddenly, he doesn't seem so smart.

Having a soaring intellect doesn't necessarily translate into a brilliant career. For proof, look at a list of Mensa members. Mensa, a society for people who've scored in the top 2 percent of standardized I.Q. tests, numbers about 100,000, most of whom you've never heard of. Marilyn Vos Savant, a Mensa member, is listed in Guinness World Records as having the highest I.Q. ever recorded. What has she accomplished, other than being famous for her I.Q. score? Actor James Woods is also in Mensa. But if he's so smart, why did he agree to play the lead in the squirm-inducing 2003 TV movie Rudy: The Rudy Giuliani Story?

The kind of brilliance we're looking at is not measured in I.Q. (View our lists of game changers, connectors, tastemakers, rebels, and upstarts.) It manifests itself in work that is changing entire industries and influencing others. Some people are brilliant beyond dispute—Edison, Einstein, Mozart, Twain—but such cases are rare, freakish spikes amid the range of normal genetic variations. Is there anyone in business today who could stand with an Edison or an Einstein? Even though we've left Bill Gates and Warren Buffett off our list in favor of those who are changing business, conventional wisdom labels both brilliant. Both are intellectually stellar, though in different ways. Gates loves to wow people by tossing around his deep knowledge of everything from software code to art. Buffett seems to work hard to make sure he doesn't come across as supersmart. His brilliance, says Xerox C.E.O. Anne Mulcahy, is in "making practical sense of issues that other leaders tend to make too complex." It's the brilliance of simplicity, like the opening of Beethoven's Symphony No. 5 or the song "A Horse With No Name"—a No. 1 hit built on, what, two notes?

Challenging as it is for those of us with prosaic intellects to peg brilliance, I've sometimes wondered, Do the brilliant think of themselves as brilliant? I asked Nathan Myhrvold, C.E.O. of Intellectual Ventures and widely considered to be one of the smartest people in technology, if he is brilliant. He said no, and as expected, gave me a brilliant answer. "If you put yourself in that camp, you might be correct," he teased. "But then, you're also an asshole."